We will now prove that the universal tropical Jacobian \(\mathcal {J}^{trop}_{g,n}\)  is a cone stack, i.e. a geometric stack over \(\mathbf {RPCC}\)  (see [1]}). We will achieve this by describing it as a combinatorial cone stack in the sense of [1]}, and then use that cone stacks are equivalent to combinatorial cone stacks by [1]}.
The analogous description for \(\mathcal {M}^{trop}_{g,n}\)  is proved in [1]} and it realizes \(\mathcal {M}^{trop}_{g,n}\)  as the cone stack associated to the combinatorial cone stack
\(\begin{aligned}\Gamma _{\operatorname{\mathcal {SG}}_{g,n}}: \operatorname{\mathcal {SG}}_{g,n}^{\operatorname{opp}}& \longrightarrow \operatorname{\bf {RPC}}^f\\G & \longmapsto \mathbb {R}_{\ge 0}^{E(G)},\\\big (\pi :G\rightarrow G^{\prime } \big )& \longmapsto \big (\mathbb {R}_{\ge 0}^{E(G^{\prime })}\hookrightarrow \mathbb {R}_{\ge 0}^{E(G)}\big )\end{aligned}\) 
